Observations of transiting gas giant exoplanets have revealed a pervasive depletion of methane, which has only recently been identified atmospherically. The depletion is thought to be maintained by disequilibrium processes such as photochemistry or mixing from a hotter interior. However, the interiors are largely unconstrained along with the vertical mixing strength and only upper limits on the CH₄ depletion have been available. The warm Neptune WASP-107 b stands out among exoplanets with an unusually low density, reported low core mass, and temperatures amenable to CH₄ though previous observations have yet to find the molecule. Here we present a JWST NIRSpec transmission spectrum of WASP-107 b which shows features from both SO₂ and CH₄ along with H₂O, CO₂, and CO. We detect methane with 4.2σ significance at an abundance of 1.0±0.5 ppm, which is depleted by 3 orders of magnitude relative to equilibrium expectations. Our results are highly constraining for the atmosphere and interior, which indicate the envelope has a super-solar metallicity of 43±8× solar, a hot interior with an intrinsic temperature of Tᵢₙₜ=460±40 K, and vigorous vertical mixing which depletes CH4 with a diffusion coefficient of Kzz = 1011.6±0.1 cm²/s. Photochemistry has a negligible effect on the CH₄ abundance, but is needed to account for the SO₂. We infer a core mass of 11.5-3.6+3.0 M_, which is much higher than previous upper limits, releasing a tension with core-accretion models.
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